The FA have a good record of getting rid of managers just when things are looking up (Robson in 1990, Venables in 1996 and Hoddle in 1999). They also excel in not appointing the people's choice such as Clough and Redknapp though Keegan did get his chance before Euro2000.
They sacked Alf Ramsay in 1973 which, while understandable on some levels, in part led to England failing to qualify two further tornaments. After winning the World Cup they could've at least engineered a dignified exit.
Don Revie buggered off to the Middle East when the going got tough but you wonder what might have been if Ramsay had stayed. Poland finished third in 1974, Czechoslovakia won in 1976 and Italy came fourth in 1978. On each occasion England failed to qualify against those three teams either on goal difference, or for the want of a single goal.
We weren't that far away in the 70s. English sides won three European Cups, five UEFA/Fairs Cups and two Cup Winners' Cups during that decade. We also had five runners up during the same period. The FA has always been like this though ever since they declined to enter the World Cup in 1930 - just so arrogant.